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Math Help - Help with solving three trig equations

  1. #1
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    Help with solving three trig equations

    Hey guys, I'm in a college trig class and these questions were on my last test. I thought I had trig identities down but I barely know where to start on these ones. Can you help me out?

    1. 12sin(2t)cos(3t)+20sin(2t)-cos(3t)-5=0
    2. 6sec(2t)^2-13sec(2t)=6
    3. 2sin(x)cos(-x)=2sin(-x)sin(x)
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  2. #2
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    Re: Help with solving three trig equations

    Quote Originally Posted by Aghori2402 View Post
    Hey guys, I'm in a college trig class and these questions were on my last test. I thought I had trig identities down but I barely know where to start on these ones. Can you help me out?

    1. 12sin(2t)cos(3t)+20sin(2t)-cos(3t)-5=0
    2. 6sec(2t)^2-13sec(2t)=6
    3. 2sin(x)cos(-x)=2sin(-x)sin(x)
    For the second, write \displaystyle \begin{align*} x = \sec{2t} \end{align*}, which gives \displaystyle \begin{align*} 6x^2 - 13x = 6 \end{align*}. Solve this quadratic equation for \displaystyle \begin{align*} x \end{align*}, which tells you what \displaystyle \begin{align*} \sec{2t} \end{align*} equals, which you can use to find \displaystyle \begin{align*} t \end{align*}.

    For the third

    \displaystyle \begin{align*} 2\sin{(x)}\cos{(-x)} &= 2\sin{(-x)}\sin{(x)} \\ 2\sin{(x)}\cos{(-x)} - 2\sin{(-x)}\sin{(x)} &= 0 \\ 2\sin{(x)}[\cos{(-x)} - \sin{(-x)}] &= 0 \\ \sin{(x)} = 0 \textrm{ or } \cos{(-x)} - \sin{(-x)} &= 0 \end{align*}

    Solve each of these equations for \displaystyle \begin{align*} x \end{align*}.
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  3. #3
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    Re: Help with solving three trig equations

    For no. 3 Use cos(-x)=cosx and sin(-x)=-sinx
    So question becomes 2sinxcosx=-2sinxsinx Cancel 2 and get sinxcosx+sinxsinx=0
    sinx(cosx+sinx)=0 So sinx=0 or cosx+sinx=0 giving sinx=-cosx giving sinx/cosx=-1 That is tanx=-1
    So sinx-0 or tanx=-1 Give the answers for x in whatever range you were asked.
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    Re: Help with solving three trig equations

    Quote Originally Posted by Aghori2402 View Post

    1. 12sin(2t)cos(3t)+20sin(2t)-cos(3t)-5=0
    If the question had been 12\sin(2t)\cos(3t)+20\sin(2t)-3cos(3t)-5=0 I would have said factorise.
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